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arXiv · 1902.02559

Optimal design strategy for non-Abelian geometric phases using Abelian gauge fields based on quantum metric

Mark Kremer·Lucas Teuber·Alexander Szameit·Stefan Scheel
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Abstract

Geometric phases, which are ubiquitous in quantum mechanics, are commonly more than only scalar quantities. Indeed, often they are matrix-valued objects that are connected with non-Abelian geometries. Here we show how generalized, non-Abelian geometric phases can be realized using electromagnetic waves travelling through coupled photonic waveguide structures. The waveguides implement an effective Hamiltonian possessing a degenerate dark subspace, in which an adiabatic evolution can occur. The associated quantum metric induces the notion of a geodesic that defines the optimal adiabatic evolution. We exemplify the non-Abelian evolution of an Abelian gauge field by a Wilson loop.

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Mark Kremer, Lucas Teuber, Alexander Szameit, Stefan Scheel. 2019-02-07. Optimal design strategy for non-Abelian geometric phases using Abelian gauge fields based on quantum metric. https://doi.org/10.1103/physrevresearch.1.033117

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